1. What is the Black Hole Lifetime Equation?

The Black Hole Lifetime Equation estimates how long a black hole of given mass would take to evaporate via Hawking radiation at a given temperature. It's derived from quantum field theory in curved spacetime.

2. How Does the Calculator Work?

The calculator uses the black hole lifetime equation:

Where:

• \( t \) — Lifetime (seconds)
• \( \hbar \) — Reduced Planck constant (1.0545718 × 10⁻³⁴ J·s)
• \( c \) — Speed of light (299,792,458 m/s)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M \) — Black hole mass (kg)
• \( k \) — Boltzmann constant (1.380649 × 10⁻²³ J/K)
• \( T \) — Temperature (K)

Explanation: The equation shows that more massive black holes live longer and evaporate more slowly, while hotter black holes evaporate faster.

3. Importance of Black Hole Lifetime Calculation

Details: Calculating black hole lifetimes helps understand Hawking radiation, black hole thermodynamics, and the ultimate fate of black holes in the universe.

4. Using the Calculator

Tips: Enter black hole mass in kilograms and temperature in kelvins. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why does the lifetime depend on mass and temperature?
A: More massive black holes have lower temperatures and radiate less energy, so they evaporate much more slowly.

Q2: What is the typical lifetime of a black hole?
A: A solar-mass black hole would take about 10⁶⁷ years to evaporate, while microscopic black holes evaporate almost instantly.

Q3: What happens at the end of a black hole's life?
A: As the black hole loses mass, it evaporates faster until it explodes in a burst of high-energy radiation.

Q4: Are there limitations to this equation?
A: The equation assumes a non-rotating, uncharged black hole in empty space with no matter falling in.

Q5: Can we observe black hole evaporation?
A: Not currently, as even the hottest known black holes would take much longer than the age of the universe to evaporate significantly.